The Boston Globe is dropping its lawsuit against a former staff member who alleged that the paper’s editor, Brian McGrory, sent her an inappropriate text, saying in a letter to the court that “a preliminary injunction is no longer necessary,’’ and expressing hope that the former employee will voluntarily cooperate with the paper’s investigation into her charges.

The Globe in May filed for an injunction against Hilary Sargent, a former writer and editor for the Globe-owned website Boston.com, seeking to compel her to answer questions about her allegations against McGrory. The newspaper had argued that Sargent’s 2016 separation agreement from the company required her “reasonable’’ cooperation with any investigation arising from her employment.

The Globe filed its complaint days after Sargent posted a screenshot of a text exchange on Twitter in which one of the parties asks the other, “What do you generally wear when you write?’’ She has attributed the question to McGrory.

With the suit being withdrawn, Sargent suggested Monday in a statement that she would cooperate: “I look forward to speaking openly without the threat of litigation, and in a manner that takes into account the sensitivity of the subject matter.’’

After a hearing in Suffolk Superior Court on Thursday, Judge Christine M. Roach directed the parties to jointly update her on the status of the dispute by week’s end, before she began to write her ruling.

In that letter to the judge, dated last Friday, the newspaper said that it only reluctantly filed the lawsuit seeking Sargent’s cooperation after the paper’s repeated requests for answers were unsuccessful in the days after Sargent posted the allegation. The lawsuit “has largely succeeded in achieving its purpose,’’ the Globe wrote, by eliciting information from Sargent in court documents: Her filings indicate she does not have the original text exchange, and that she does not recall the date of the exchange and that it may have occurred after she left Boston.com. She also confirmed that she and McGrory used to date.

“The Globe remains hopeful for its outside investigator to interview Ms. Sargent so as to hear directly from her concerning her allegations regarding Mr. McGrory and to review all pertinent information she may possess,’’ the newspaper’s lawyer, Mark Batten, wrote to Roach. “But the Globe is also confident that it has now taken all steps reasonably available to it, and has learned significant new information as a result that will assist the Globe in reaching sound conclusions about Ms. Sargent’s allegation.’’

The Globe on Monday filed a motion to voluntarily dismiss the suit.

In a filing, Sargent’s lawyer Jack Siegal called the lawsuit and its motions “premature, heavy-handed, and misguided efforts to obtain supposed cooperation — which Ms. Sargent has never refused to provide. She simply refused to discuss the matter prior to obtaining counsel.’’

“The Globe’s attempt to explain their withdrawal by suggesting Ms. Sargent has in any way misled the public or refused to cooperate is yet again simply an effort to save face publicly while admitting they should never have filed the action in the first instance. Ms. Sargent has always been at the vanguard of raising awareness of inappropriate behavior at the Globe and remains open to speaking with the Globe — but without litigation and threats of reprisal,’’ Siegal said.

In a statement issued Monday, the Globe repeated a number of points from its letter to Judge Roach.

“The action’s purpose was to ascertain the truth about a serious allegation Ms. Sargent publicly leveled on social media regarding an inappropriate text exchange between her and Boston Globe Editor Brian McGrory,’’ the paper said. “In her tweet, she implied that it was sent while she was an employee at boston.com, although there was no date visible.

“Faced with Ms. Sargent’s refusal to provide the date of the exchange, the Globe brought legal action to expeditiously learn all relevant information from Ms. Sargent. That legal action succeeded in achieving its purpose: Ms. Sargent has finally provided the information the Globe has requested from the start. Crucially, Ms. Sargent has now admitted that she does ‘not recall’ when the messages were sent and it is ‘more likely’ that they were sent after she worked at the Globe.’’

Sargent has said in court filings that the screenshot she posted on Twitter was indicative of “inappropriate and sexually suggestive’’ messages McGrory sent her while she worked at Boston.com. The filing did not provide other text messages.

McGrory’s lawyer, Martin Murphy, said in a statement Monday that “Brian McGrory has fully cooperated, will continue to fully cooperate, and knows, as he’s said all along, that he has never harassed a Globe colleague or anyone else in his life.’’

Sargent was a writer and editor at Boston.com from 2014 to 2016.

In a statement posted Monday on social media, Sargent repeated her recent statements that she had approached Globe management last fall about discussing sexual harassment at the company, but that her requests were ignored.

“It wasn’t until I went public last month with an accusation that the Globe contacted me, and immediately threatened litigation,’’ she said. “I have never refused to cooperate in the Globe’s ‘investigation.’ No media institution that expects to be taken seriously on the issue of sexual harassment should ignore concerns of one of its former employees, nor should they resort to litigation as a first option. I am disappointed that the Globe’s leadership chose that route, and I’m pleased they chose to drop this lawsuit.’’

Mark Arsenault can be reached at mark.arsenault@globe.com